I think it would register no recognition to the majority of American English speakers. It is a French loan word used essentially only in open source contexts because we don't have an equivilent ("free" is way more ambiguous is meaning).
The only negative connotation I know of is the association with some overzealous nerdy kids who find out the difference between libre and gratis and loudly bring it up all the time.
Italy here. "Libre" sounds spanish to me. I realized only now that french has the same word (and I read it many times), but probably the final e is silent. I pronounce it, so it's spanish. Apparently it's the correct way: https://lwn.net/Articles/408141/
When I first saw LibreOffice I first thought it was a take on the comedy movie Nacho Libre. And I studied French, so you'd think that would help but not really.
Though the French pronunciation differs as the IPA shows /libʀ/ which is rather different than spanish /ˈliβɾe/. So its one of those "final e is silent, with a french twist" words that were maddening to learn after German where that almost never happens.
I don't no much French but I think in this case the final e is not silent but also not stressed. Stress is on the i, same as in the Spanish pronunciation I think.
I speak en-AU - I'm not sure what connotations "libre" has to most English speakers who haven't learned a Romance language or been involved in the Free Software world. "Libre" is not a common English word - I imagine to many English speakers you'd probably have to explain the shared etymology with "liberty" for people to get it. The French pronunciation is non-obvious to an English speaker.
I don't think it has any connotation for most Americans. It isn't a word that is commonly used. I imagine that they hear it and think "Lee Bray" or Luche Libre wrestling.
Oh wait, I just had a thought: Luche Libre Office. That's is an awesome idea.
It's an unfortunate side effect of FSF's fascination with being uber-precise around terms like "free" and "open". Because English doesn't offer sufficient nuance here, and Stallman really, really hates it when people get the implications that were not intended, he had to go look for, or create, a word that would be unambiguously "free as in freedom" (by FSF definition of freedom, anyway). And so he did - with the unfortunate side effect that no English speaker outside of that community knows neither the word nor the meaning.
Most Americans don't know what Libre means. It just sounds like a European word... French or Spanish, perhaps. They also don't know how to pronounce it... Lee-Bray-Office, Lee Brooff-iss, Li-berr-office? It always felt like a missed opportunity when they chose that name.
